The $SO(10)$ group is spontaneously broken down into the Standard Model gauge group at around $10^{16}$ GeV and the electroweak scale is ~246 GeV. I think there should be 45 gauge fields predicted by an $SO(10)$ GUT (from $\frac{1}{2}N(N-1)$ generators, with $N=10$). How many of them would experience SSB and therefore acquire mass at scales above the electroweak scale?
Gauge Theory – Number of Gauge Fields with Masses Above Electro-Weak Scale in SO(10) GUT
beyond-the-standard-modelgauge-theorygrand-unificationgroup-theorysymmetry-breaking
Related Solutions
I think you have understood it almost well.
The masses do not change, they are what they are; at least at colliders. At high energy, it is true that the impact of masses and, more generally, of any soft term, becomes negligible. The theory for $E\gg v$ becomes very well described by a theory that respects the whole symmetry group.
Notice that to do so consistently in a theory of massive spin $-1$, you have to introduce the Higgs field as well at energies above the symmetry breaking scale. For the early universe, the story is slightly different because you are not in the Fock-like vacuum, and there are actual phase transitions (controlled by temperature and pressure) back to the symmetric phase where in fact the gauge bosons are massless (except perhaps for a thermal mass, not sure about it).
EDIT
I'd like to edit a little further about the common misconception that above the symmetry breaking scale gauge bosons become massless. I am going to give you an explicit calculation for a simple toy mode: a $U(1)$ broken spontaneously by a charged Higgs field $\phi$ that picks vev $\langle\phi\rangle=v$. In this theory we also add two dirac fields $\psi$ and $\Psi$ with $m_\psi\ll m_\Psi$. In fact, I will take the limit $m_\psi\rightarrow 0$ in the following just for simplicity of the formulae. Let's imagine now to have a $\psi^{+}$ $\psi^-$ machine and increase the energy in the center of mass so that we can produce on-shell $\Psi^{+}$ $\Psi^{-}$ pairs via the exchange in s-channel of the massive gauge boson $A_\mu$. In the limit of $m_\psi\rightarrow 0$ the total cross-section for $\psi^-\psi^+\rightarrow \Psi^-\Psi^+$ is given (at tree-level) by $$ \sigma_{tot}(E)=\frac{16\alpha^2 \pi}{3(4E^2-M^2)^2}\sqrt{1-\frac{m_\Psi^2}{E^2}}\left(E^2+\frac{1}{2}m_\Psi^2\right) $$ where $M=gv$, the $A_\mu$-mass, is given in terms of the $U(1)$ charge $g$ of the Higgs field. In this formula $\alpha=q^2/(4\pi)$ where $\pm q$ are the charges of $\psi$ and $\Psi$. Let's increase the energy of the scattering $E$, well passed all mass scales in the problem, including $M$ $$ \sigma_{tot}(E\gg m_{i})=\frac{\pi\alpha^2}{3E^2}\left(1+\frac{M^2}{2E^2}+O(m_i^2/E^4)\right) $$ Now, the leading term in this formula is what you would get for a massless gauge boson, and as you can see it gets correction from the masses which are more irrelevant as $m_i/E$ is taken smaller and smaller by incrising the energy of the scattering. Now, this is a toy model but it shows the point: even for a realistic situation, say with a GUT group like $SU(5)$, if you scatter multiplets of $SU(5)$ at energy well above the unification scale, the masses of the gauge bosons will correct the result obtained by scattering massless gauge bosons only by $M/E$ to some power.
Answer to the main question:
It is a well regarded fact that the terminology unified electroweak interaction is a bit of an abuse of terminology. What the term means is that both Quantum Field Theories, the Hypercharge ($U(1)_Y$) and Weak ($SU(2)_L$), are unified in a common framework, which predicts the low energy electromagnetism ($U(1)_{em}$) through the Higgs mechanism $$ U(1)_Y \times SU(2)_L \to U(1)_{em}$$ It does not refer to an unification scenario as in the Grand Unified Theory (GUT) setup, it's meant to refer to an unification in the sense Weak decays and Electromagnetism are understood as remnants of a higher-energy theory, the Standard Model.
In comparison with GUTs the terminology can be applied if you think that regular GUT setups predict unification into a gauge group which is composed of solely one (semi) simple Lie group, e.g. $SU(5)$, $SO(10)$ being 2 of the most popular. In this sense the couplings do unify. The electroweak unification can be regarded as a unification into a group with 2 (semi) simple Lie group factors, the $SU(2)$ and $U(1)$. It is in this way of thinking about it that people refer to as unification. Notice that in the later case each factor can has its own coupling, and so the couplings are not equal, i.e. do not unify.
Answer to the bonus question:
What you asked is a big open question. Fermionic masses come from Lagrangian terms called Yukawa couplings, for example for the electron $$ y H L e+\mbox{h.c.}$$ for example, and the masses are then $$ m \sim v y$$ where $v$ is the vacuum expectation value of the Higgs field, $H$, and $y$ are the Yukawa couplings are not specified in the Standard Model and one should expect them to be of order 1. But this only happens to the top quark, while all the other fermions have a lot smaller (in some cases many orders of magnitude smaller) than 1. Why this is like this is still an open question in Physics.
Best Answer
Above the SM SSB scale of 1/4 TeV, there are 8+3+1 = 12 massless gauge bosons; so, in your model, all other massive elementary vector bosons correspond to SSBroken generators, which makes them 45-12= 33 in all, all the way to "the" GUT scale, past which there are no more massive vectors. The GUT scale may involve several steps of partial braking to SU(5)$\times$ U(1), etc., but the takeaway point is that a few orders of magnitude below all of these scales, you must have 33 massive vectors.
Is this what you are after?